Solve for the variable. 6(7 + 2) − 17b = b

In the game Divider-chooser, as the name implies, one player, referred to as the dividers, divides S into two parts, and the other player, referred to as the dropdown, selects the share they desire while leaving the other share up for the spacer to decide.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

In our instance, Fred and Maria will share a cake in this way.

Without regard to the type of cake, they each prefer, Fred offers to split the cake into 10 equal pieces as the first option.

Maria, the chooser, got to pick any seven pieces to get her fair portion. Fred will get the final three pieces. Maria will have better options with this strategy because she is a picky person.

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The depths below sea level, the rising speed, and the available air

supply, determine the minimum depth Ursula can wait.

Correct response;

The given parameters;

The initial depth of Prince Eric = 250 feet below sea level

Duration of air supply available = 10 minutes

Speed of ascent of Prince Eric = 20 ft./minute

The depth at which Ursula is forced to wait = 100 feet below sea level

The maximum ascent possible with the available air supply is given as follows;

Ascent = 20 ft./min × 10 min. = 200 ft.

Therefore, the air supply is insufficient to swim to the surface.

Level at which Ursula waits = 100 ft.

Level to which Prince Eric requires to ascent = 250 ft. - 100 ft. = 150 ft.

\(Time \ it \ takes \ to \ ascent \ to \ 150 \, ft. = \dfrac{150 \, ft.}{20 \, ft./min} = \mathbf{7.5 \,min}\)

The time it will take Prince Eric to ascend to Ursula's level is 7.5 minutes,

which is less than the 10 minutes, time to use the available air supply.

Therefore;

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As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of depression increases.

the arc formed as the line of sight drops from the horizon. The angle of depression is the angle formed when an object is perceived below the observer's height between the horizon and the line of sight of the observer. The depression angle is the angle formed between the line of sight looking down at the object and the horizontal line of sight. If you are on a hill or a building and you are looking down at something, you can tell the slope. To measure these angles, a theodolite or an inclinometer might be employed.

As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of the depression increases.

∠x = 65° ≤ ∠XYZ

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Answer: Height = 20 inches, Width = 36 inches

Step-by-step explanation:

Let the height be \(h\) and the width be \(h+16\).

Using the formula for the perimeter of a triangle,

\(2(h+h+16)=112\\\\2(2h+16)=112\\\\2h+16=56\\\\2h=40\\\\h=20 \implies h+16=36\)

Answer:

1.(f+g)(x)=5x-11

2.(f-g)(x)=x-3

Step-by-step explanation:

1.(f+g)(x)=f(x)+g(x)

=(3x-7)+(2x-4)

=5x-11

2.(f-g)(x)=f(x)-(g)

=(3x-7)-(2x-4)

=3x-7-2x+4

=x-3

The value of the functions (f + g)(x) and (f - g)(x) will be 5x - 11 and x - 3.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The functions are given below.

f(x) = 3x - 7

g(x) = 2x - 4

The value of the function (f + g)(x) will be

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 3x - 7 + 2x - 4

(f + g)(x) = 5x - 11

The value of the function (f - g)(x) will be

(f - g)(x) = f(x) - g(x)

(f - g)(x) = 3x - 7 - (2x - 4)

(f - g)(x) = 3x - 7 - 2x + 4

(f - g)(x) = x - 3

Thus, the value of the functions (f + g)(x) and (f - g)(x) will be 5x - 11 and x - 3.

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Step-by-step explanation:

z+w= 1+3i-3-4i = -2-i

w+z=-3-4i+1+3i = -2-i

So, z+w = w+z

So, complex number addition is commutative

If z = 1 + 3i and w = -3 - 4i, then z + w = - 2 - i and w + z = - 2 - i, which supports that complex number addition is commutative.

We are aware that the addition's commutative property states that altering the addends' order will not affect the sum.

Here z = 1 + 3i and w = -3 - 4i.

Now, z + w = 1 + 3i - 3 - 4i = 1 - 3 + 3i - 4i = - 2 - i

and w + z = - 3 - 4i + 1 + 3i = - 3 + 1 - 4i + 3i = - 2 - i

i.e. z + w = w + z

Clearly, the addition obeys the commutative property.

Therefore we can conclude that If z = 1 + 3i and w = -3 - 4i, then z + w = - 2 - i and w + z = - 2 - i, which supports that complex number addition is commutative.

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The area of ΔQRS is 26.10 square units.

What is triangle?

A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles.

To find the area of \($\triangle QRS$\), we can use the formula:

\($Area = \frac{1}{2} \times base \times height$\)

where the base and height are the length of two sides of the triangle that are perpendicular to each other. We can find these sides using trigonometry.

First, we need to find the length of side \($QR$\). We can use the Law of Cosines:

\($QR^2 = QS^2 + RS^2 - 2(QS)(RS)\cos(R)$\)

where \($R$\) is the angle at vertex \($R$\). Substituting the given values, we get:

\($QR^2 = 9^2 + 5^2 - 2(9)(5)\cos(57^\circ)$\)

\($QR \approx 8.02$\)

Next, we need to find the height of the triangle, which is the perpendicular distance from vertex \($R$\) to side \($QS$\). We can use the sine function:

\($\sin(R) = \frac{opposite}{hypotenuse}$\)

\($\sin(57^\circ) = \frac{height}{8.02}$\)

\($height \approx 6.51$\)

Now we can find the area of the triangle:

\($Area = \frac{1}{2} \times QR \times height$\)

\($Area = \frac{1}{2} \times 8.02 \times 6.51$\)

\($Area \approx 26.10$\) square units

Therefore, the area of \($\triangle QRS$\) is approximately \($26.10$\) square units.

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Answer:

c pls tell me if I'm right or wrong

Answer:

$54

Step-by-step explanation:

The amount of the discount can be found by multiplying 180 by 0.3 which is 54.

If you also need to know the new total it would be $126 because

180 - 54 = 126

Answer:

exercising is good

Step-by-step explanation:

exercising releases hormones in your body that can make you happier, it also keeps your mind in tip top shape. Also even just being outside of a building would also release hormones in your brain that causes you to lighten your mood!

Answer: Exercise can help with mental health because when your angry sometimes working out can help get rid of anger and if your sad it can help get more motivated and positive about some stuff. It also helps with discipline and respect which can help with your social skills by talking respectfully to others.

Answer: any negative value

Step-by-step explanation:

g(x)= ax², inc on x<0 & dec on x>0

Firstly we need to get the derivative of g(x)

g'(x)=2ax

for inc interval g'(x) should be +ve

x<0 (i.e. x= -ve), then a must be -ve

for dec interval g'(x) should be +ve

x>0 (i.e. x= +ve), then a must be -ve

so in both cases a must be a negative constant

Answer:

The sales tax is determined by computing a percent of the purchase price. To find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price.

Step-by-step explanation:

Answer  

wjiehnjshude

Step-by-step explanation:

Answer:

-5/6

Step-by-step explanation:

(9, 5) and (21, -5)

slope = m = (difference in y)/(difference in x)

m = (-5 - 5)/(21 - 9)

m = -10/12

m = -5/6

Answer: -5/6

The slope of the line that passes through points (9,5) and (21,-5) is -5/6.

We can use the two-point formula to find the slope for the given line. The formula is as follows:

(y2 - y1) = m*(x2 - x1)

Where (x1, y1, x2, and y2) represent the points on the line, and m is the slope of the line.

In the given case:

x1=9, x2=21

y1=5, y2=-5

Using these values in the two-point formula, we get:

(-5-5)=m*(21-9)

-10=m*12

m=-10/12

m=-5/6

Hence the slope of the line is -5/6.

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The solution of the equation 4x - 3  = 5 is not extraneous .

Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation.

Therefore, let's solve the equation to know whether it is extraneous solution.

Hence,

4x - 3  = 5

add 3 to both sides of the equation

4x - 3 + 3 = 5 + 3

4x = 8

divide both sides of the equation by 4

4x / 4 = 8 / 4

x = 2

Therefore, it is not extraneous solution.

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Answer:

-----------------------------

Given sequence:

If t(n) = 200, we can try to find the value of n:

There is no integer solution, since 32 < 40 < 64 or 2⁵ < 40 < 2⁶, the value of n should be between 5 and 6.

The sequence should include integer numbers, so there is no solution.

Given function:

Solve for x if f(x) is 200:

Answer:

1.  No

\(\textsf{2.} \quad x=\dfrac{\ln 40}{\ln 2} \approx5.32\;(\sf 2\;d.p.)\)

Step-by-step explanation:

Given sequence:

\(t(n)=5 \cdot 2^n\)

To determine if the sequence has a term with a value of 200, substitute t(n)=200 into the equation and solve for n:

\(\implies 5 \cdot 2^n=200\)

\(\implies 2^n=40\)

\(\implies \ln 2^n=\ln 40\)

\(\implies n\ln 2=\ln 40\)

\(\implies n=\dfrac{\ln 40}{\ln 2}\)

\(\implies n=5.3219280...\)

In a sequence, n is a positive integer.  Therefore, it is not possible for the sequence to have a term with the value of 200, as when t(n)=200, n is not a positive integer.

Given function:

\(f(x)=5 \cdot 2^x\)

To determine if the function has an output of 200, substitute f(x)=200 into the function and solve for x:

\(\implies 5 \cdot 2^x=200\)

\(\implies 2^x=40\)

\(\implies \ln 2^x=\ln 40\)

\(\implies x=\dfrac{\ln 40}{\ln 2}\)

\(\implies x=5.3219280...\)

Therefore, it is possible for the function to have an output of 200 when:

\(x=\dfrac{\ln 40}{\ln 2}\)

Answer:

$3+x is less than or equal to $15

Step-by-step explanation:

I can't write the sign but it's < with a line under it

Step-by-step explanation:

y≥15-3

I am not sure

The solution to the inequality is m < −1 13/15 . m is less than negative 1 and 7 over 15

In this question we have to solve for the inequality that is given as m + 1/5 < -1 2/3

We would have to rewrite the equation using the math tool

\(m +\frac{1}{5}\leq 1\frac{2}{3}\)

The mixed fraction can be properly rewritten  as improper fraction

\(m +\frac{1}{5}\leq \frac{5}{3}\)

subtract 1/5 from 5/3

\(m\leq -\frac{5}{3} -\frac{1}{5}\)

we have to carry out the subtraction of the fraction

\(m < \frac{-25-3}{15}\)

\(m < \frac{-28}{15}\)

This can be written in mixed fraction as

\(m < -1\frac{13}{15}\)

Hence the solution of m is D. m < −1 13/15

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Complete question

m + 1/5 < -1 2/3

Responses

A. m > −1 13/15

m is greater than negative 1 and 13 over 15

B. m > −1 7/15

m is greater than negative 1 and 7 over 15

C. m < −1 7/15

m is less than negative 1 and 7 over 15

D. m < −1 13/15

m is less than negative 1 and 7 over 15

Answer:

see below and attachment

Step-by-step explanation:

a=30°

because, the marked angle of 30° is an alternate interior angle to angle a.  Alternate interior angles are congruent, and we know they are congruent because the 2 horizontal lines are parallel.

b=50°

because the marked angle of 50° is a vertical angle to angle b.  Vertical angles are congruent because 2 lines that intersect have opposite congruent angles, making them vertical angles to each other.

c=50°

because the marked angle of 50° is a corresponding angle (same side angle) to angle c.  These corresponding angles are congruent because the 2 horizontal lines are parallel.

d=100°

because the 3 interior angles of a triangle must add up to 180°.  We have 30°, 50°, so the last angle must be 100°.  We can also figure this out because the bottom horizontal line is a straight line, meaning the angle is also 180°.  We have angle a as 30°, angle c as 50°, so angle d must be 100°.

Hope this helps!  See attachment for visual.

Answer:

m ≤ 5

Step-by-step explanation:

I will begin by assuming m to be the number.

Then, the sum of m and 3 is: m + 3.

The symbol for "less than or equal to" is ≤.

So we form an inequality, like this :

m + 3 ≤ 8

To find m subtract 3 on each side:

m ≤ 5

Therefore, m ≤ 5.

Answer:

x^2 + 8x + 15

Step-by-step explanation:

( x + 3 ) ( x + 5 )

1. distribute

( x + 3 ) ( x + 5 )

x^2 + 3x + 5x + 15

2. simplify

x^2 + 8x + 15

Answer:

47.4 not rounded 47.38

Step-by-step explanation:

You divide 199 by 4.2 and get 47.4 and then you can multiply 47.38x4.2 and will get you 199

Step-by-step explanation:

199 =R×4.2

R= 199÷2

R= 47.38km

nearest tenth is 47.4

Answer:

D. 2914

Step-by-step explanation:

Multiply the numbers outside of the shape.

Answer:

1.29 x \(10^{9}\)

Step-by-step explanation:

{(1.8 x 10^-6) x (4.3 x 10^8)}  / [(8 x 10^-5) x (7.5 x 10^-3)]

[(1.8 x 4.3)x(10^-6 x 8)] / [(8 x 7.5) x(10^-5 x 10^ -3)]

(.129 x 10^[2-(-8)]

.129 x 10^10

1.29 x 10^-1 x 10^10

1.29 10^9

The value (9/10)*81 is greater than (5/6)*81

The values are given as:

(5/6)*81 and (9/10)*81

Remove the common factor in both values

So, we have:

5/6 and 9/10

Convert to decimals

0.83 and 0.9

0.9 is greater than 0.83

Hence, (9/10)*81 is greater than (5/6)*81

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Answer:

24 + c

Step-by-step explanation:

Answer:

45 srry if its wrong :(

Answer:

3×4

Step-by-step explanation:

12 +12=24 so that how you do it bye

A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  =  $272,090

      A) - Calculate the Percentage of the Value Remaining After the Decrease

       B) - Calculate the NEW VALUE of the house

A) - The PERCENTAGE of the VALUE REMAINING AFTER the DECREASE

      100%  -  9%  =  91%

        0.91

B) - Calculate the NEW VALUE of the house:

NEW VALUE  =  OLD VALUE  *  REMAINING PERCENTAGE

NEW VALUE  =  299,000  *  0.91

A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  = $272,090

I hope it helps!